Locality and Translations in Braided Ribbon Networks

TL;DR

This paper explores the concepts of microlocality and translations in braided ribbon networks, introducing definitions, theorems, and invariants to understand their topology and substructure relocations.

Contribution

It provides a formal framework for microlocality, introduces theorems on substructure relocation, and investigates invariants in braided ribbon networks.

Findings

Isolated substructures can be relocated within the network.

Microlocal translations are demonstrable within the framework.

Invariants have implications for the topology of braided ribbon networks.

Abstract

An overview of microlocality in braided ribbon networks is presented. Following this, a series of definitions are presented to explore the concept of microlocality and the topology of ribbon networks. Isolated substructure of ribbon networks are introduced, and a theorem is proven that allows them to be relocated. This is followed by a demonstration of microlocal translations. Additionally, an investigation into macrolocality and the implications of invariants in braided ribbon networks are presented.